# Aerodynamic Design Optimization of a Micro Radial Compressor of a Turbocharger

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## Abstract

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## 1. Introduction

## 2. Geometry Parameterization

#### 2.1. Parameterization of the Main Blade by the Beta Distribution

#### 2.2. Parameterization of Splitter Blade by LE Location

## 3. Numerical Analysis

^{5}so that a shear-stress transport (SST) turbulence model [25] was adopted near by the wall. Turbulence modelling is an important criterion to acquire precise wall shear stresses. The SST model is a combination of and has smooth transition between the k-ω and k-ε turbulence model; k-ω provides better compromises near the wall and k-ε gives a better solution in the bulk domain [25]. When using the SST model in ANSYS-CFX, ${y}^{+}$ should be under 300, so that the wall function approach is valid [26]. In this research, automatic wall function, which automatically switches from the wall-functions to low-Re near wall formulation as the mesh is refined, is used for the SST model [26].

^{−5}and imbalances in mass, momentum, and energy were below 1 × 10

^{−2}. An auto time scale was used with a scale factor of 10 to control the convergence of the solution. After approximately 600 iterations, the converged solution was obtained. Simulations were performed by a PC with a 2.00 GHz Intel Xeon CPU, and it took almost six hours to complete the simulation, depending on the geometry and convergence of the solution.

## 4. Surrogate Method with Single-Objective Optimization and Results

#### 4.1. Optimization of Main Blade

#### 4.2. Optimization of Splitter Blade

## 5. Results and Discussion

#### 5.1. Comparison of the Baseline (Base Main-Base Splitter) and Optimized Impeller (Optimized Main-Base Splitter)

#### 5.2. Comparison of the Baseline Splitter (Optimized Main-Base Splitter) and Optimized Splitter Impeller (Optimized Main-Optimized Splitter)

## 6. Conclusions

- After two consecutive optimization processes, a 2.2% efficiency improvement (1.8% based on main blade optimization, 0.4% based on LE location optimization of splitter blade) was observed at the design point as well as the near-choke point. However, similar improvements were not seen in the near-surge region.
- Beta distribution of the main blade and LE location of the splitter blade are adequate parameters to achieve dramatic aerodynamic performance by the optimization process.
- Significant aerodynamic improvement in the micro impeller after the main blade focused optimization procedure indicated that splitter blades could be independently investigated; it was not necessary to assume they were short versions of the main blade.
- Considering different parameterization method on the beta distribution could reduce design points on the fourth and higher-order Bezier curves in comparison to conventional method. Therefore, optimization performance would be increased.
- The LE location of the splitter blade is also an important parameter that enables researchers to better capture the flow and provide better blade loading at the LE, even though it does not have significant impact on the efficiency.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Definition of beta (β) distribution and the meridional contour of the impeller and location of splitter leading edge.

**Figure 4.**Meridional position of the leading edge of the splitter blade for the base centrifugal compressor.

**Figure 8.**Goodness-of-fit of the response surface using non-parametric regression and the response surface of ${\beta}_{h,\text{}LE}$(${\beta}_{h1}$)–${\beta}_{h,\text{}TE}$(${\beta}_{h2}$) on the efficiency.

Geometric Specifications | Value |
---|---|

Impeller inlet hub diameter | 9 mm |

Impeller inlet tip diameter | 24 mm |

Impeller exit tip diameter | 32.5 mm |

Impeller exit width | 2.4 mm |

Number of blades main/splitter | 5/5 |

Design Parameters | Boundary Values |
---|---|

${\beta}_{h,LE}$ | 55° ≤ ${\beta}_{h,LE}$ ≤ 65° |

$\mathrm{\Delta}{\beta}_{h}$ | 30° ≤ $\mathrm{\Delta}{\beta}_{h}$ ≤ 60° |

${\beta}_{h,max}$ | 70° ≤ ${\beta}_{h,max}$ ≤ 76° |

${\beta}_{h,TE}$ | 50° ≤ ${\beta}_{h,TE}$ ≤ 60° |

${\beta}_{s,LE}$ | 25° ≤ ${\beta}_{s,LE}$ ≤ 35° |

$\mathrm{\Delta}{\beta}_{s}$ | 0° ≤ $\mathrm{\Delta}{\beta}_{s}$ ≤ 5° |

${\beta}_{s,max}$ | 45° ≤ ${\beta}_{s,max}$ ≤ 55° |

${\beta}_{s,TE}$ | 35° ≤ ${\beta}_{s,TE}$ ≤ 50° |

$d{m}_{hub}$ | 0% ≤ $d{m}_{hub}$ ≤ 55% |

$d{m}_{shr}$ | 0% ≤ $d{m}_{shr}$ ≤ 55% |

Size Factor in Mesh Size Tab | Total Element Size | Computational Time | Iteration | Isentropic Efficiency | Pressure Ratio |
---|---|---|---|---|---|

1.1 | 1,272,054 | 364 min | 670 | 74.64% | 1.99 |

1 | 952,786 | 301 min | 570 | 74.15% | 1.98 |

0.9 | 680,744 | 282 min | 635 | 73.58% | 1.97 |

0.8 | 408,109 | 184 min | 528 | 73.02% | 1.96 |

0.7 | 300,372 | 176 min | 571 | 72.8% | 1.95 |

Design Parameters | $\text{}{\mathit{\beta}}_{\mathit{h},\mathit{L}\mathit{E}}$ | $\text{}\mathbf{\Delta}{\mathit{\beta}}_{\mathit{h}}$ | $\text{}{\mathit{\beta}}_{\mathit{h},\mathit{m}\mathit{a}\mathit{x}}$ | $\text{}{\mathit{\beta}}_{\mathit{h},\mathit{T}\mathit{E}}$ | $\text{}{\mathit{\beta}}_{\mathit{s},\mathit{L}\mathit{E}}$ | $\text{}\mathbf{\Delta}{\mathit{\beta}}_{\mathit{s}}$ | $\text{}{\mathit{\beta}}_{\mathit{s},\mathit{m}\mathit{a}\mathit{x}}$ | $\text{}{\mathit{\beta}}_{\mathit{s},\mathit{T}\mathit{E}}$ |
---|---|---|---|---|---|---|---|---|

Optimal Values | 55.3° | 53.8° | 71.9° | 54.6° | 25.6° | 2.3° | 52.9° | 45.9° |

Design Parameters | Baseline Impeller | Optimized Impeller |
---|---|---|

${\beta}_{h,LE}$ | 58° | 55.3° |

$\mathrm{\Delta}{\beta}_{h}$ | 44° | 53.8° |

${\beta}_{h,max}$ | 71° | 71.9° |

${\beta}_{h,TE}$ | 54° | 54.6° |

${\beta}_{s,LE}$ | 28° | 25.6° |

$\mathrm{\Delta}{\beta}_{s}$ | 3° | 2.3° |

${\beta}_{s,max}$ | 48° | 52.9° |

${\beta}_{s,TE}$ | 42.5° | 45.9° |

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**MDPI and ACS Style**

Atac, O.F.; Yun, J.-E.; Noh, T.
Aerodynamic Design Optimization of a Micro Radial Compressor of a Turbocharger. *Energies* **2018**, *11*, 1827.
https://doi.org/10.3390/en11071827

**AMA Style**

Atac OF, Yun J-E, Noh T.
Aerodynamic Design Optimization of a Micro Radial Compressor of a Turbocharger. *Energies*. 2018; 11(7):1827.
https://doi.org/10.3390/en11071827

**Chicago/Turabian Style**

Atac, Omer Faruk, Jeong-Eui Yun, and Taehyun Noh.
2018. "Aerodynamic Design Optimization of a Micro Radial Compressor of a Turbocharger" *Energies* 11, no. 7: 1827.
https://doi.org/10.3390/en11071827